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Human pluripotent stem cells hold great promise for developments in regenerative medicine and drug design. The mathematical modelling of stem cells and their properties is necessary to understand and quantify key behaviours and develop non-invasive prognostic modelling tools to assist in the optimisation of laboratory experiments. Here, the recent advances in the mathematical modelling of hPSCs are discussed, including cell kinematics, cell proliferation and colony formation, and pluripotency and differentiation.

The development of traction-force microscopy, in the past two decades, has created the unprecedented opportunity of performing direct mechanical measurements on living cells as they adhere or crawl on uniform or micro-patterned substrates. Simultaneously, this has created the demand for a theoretical framework able to decipher the experimental observations, shed light on the complex biomechanical processes that govern the interaction between the cell and the extracellular matrix and offer testable predictions. Contour models of cellular adhesion, represent one of the simplest and yet most insightful approach in this problem. Rooted in the paradigm of active matter, these models allow to explicitly determine the shape of the cell edge and calculate the traction forces experienced by the substrate, starting from the internal and peripheral contractile stresses as well as the passive restoring forces and bending moments arising within the actin cortex and the plasma membrane. In this chapter I provide a general overview of contour models of cellular adhesion and review the specific cases of cells equipped with isotropic and anisotropic actin cytoskeleton as well as the role of bending elasticity., Comment: 24 pages, 9 figures. arXiv admin note: text overlap with arXiv:1304.1077

Electron microscopy and X-ray diffraction studies of dormant E. coli cells revealed several forms of nucleoid condensation: quasi - nanocrystalline, quasi -liquid crystalline (or spore-like) and folded nucleosome - like structure. Of particular interest is the third type of structure since it was described here for the first time: the folded nucleosome-like. Such a structure has no relation to the toroidal DNA organization, which are the intermediate form in the formation of the quasi - nanocrystalline structure. Results observed here shed a new light both on the phenomenon of nucleoid condensation in prokaryotic cells and on the general problem of developing a response to stress. It was found out that there is no single mechanism for nucleoid condensation in the population of a dormant cell; diversity in their number, shape and packing has been seen. According to the recognized concept of a bacterial population as a multicellular organism, its heterogeneity allows to respond flexibly to the environmental changes and to survive in stressful situations. That is the reason why we observed at least three types of nucleoid condensation in dormant E. coli cells. Heterogeneity of dormant cells increases the ability of the whole population to survive under various stress conditions. For better understanding of the nucleoid condensation mechanism, it is necessary to study the reverse transition of the nucleoid in bacteria from the dormant to the functional state., Comment: 26 pages, 8 figures, 1 table

We propose a multiscale model for the invasion of the extracellular matrix by two types of cancer cells, the differentiated cancer cells and the cancer stem cells. We investigate the epithelial mesenchymal-like transition between them being driven primarily by the epidermal growth factors. We moreover take into account the transdifferentiation program of the cancer stem cells towards the cancer-associated fibroblast cells as well as the fibroblast-driven remodelling of the extracellular matrix. The proposed haptotaxis model combines the macroscopic phenomenon of the invasion of the extracellular matrix by both types of cancer cells with the microscopic dynamics of the epidermal growth factors. We analyse our model in a component-wise manner and compare our findings with the literature. We investigate pathological situations regarding the epidermal growth factors and accordingly propose "mathematical-treatment" scenarios to control the aggressiveness of the tumour.

We examine the threshold of the influence of the tunneling nanotubes (TNTs) on the cell-to-cell communication integrity. A deterministic model is introduced with the Michaelis-Menten dynamics and the intercellular exchange of substance. The influence of TNTs are considered as a functional perturbation of the main communication and treated as the matrix nearness problems. We analyze communication integrity in terms of the \emph{pseudospectra} of the exchange, to find the \emph{distance to instability}. The threshold of TNTs influence is computed for Newman-Gastner and Erd\H{o}s-R\'enyi gap junction (GJ) networks., Comment: 6 pages, 4 figures

We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated proliferation rate. Our formulation is based on an age-dependent stochastic process. Cells within the population are characterised by their age (i.e. time elapsed since they were born). The age-dependent (oxygen-regulated) birth rate is given by a stochastic model of oxygen-dependent cell cycle progression. Once the birth rate is determined, we formulate an age-dependent birth-and-death process, which dictates the time evolution of the cell population. The population is under a feedback loop which controls its steady state size (carrying capacity): cells consume oxygen which in turn fuels cell proliferation. We show that our stochastic model of cell cycle progression allows for heterogeneity within the cell population induced by stochastic effects. Such heterogeneous behaviour is reflected in variations in the proliferation rate. Within this set-up, we have established three main results. First, we have shown that the age to the G1/S transition, which essentially determines the birth rate, exhibits a remarkably simple scaling behaviour. Besides the fact that this simple behaviour emerges from a rather complex model, this allows for a huge simplification of our numerical methodology. A further result is the observation that heterogeneous populations undergo an internal process of quasi-neutral competition. Finally, we investigated the effects of cell-cycle-phase dependent therapies (such as radiation therapy) on heterogeneous populations. In particular, we have studied the case in which the population contains a quiescent sub-population. Our mean-field analysis and numerical simulations confirm that, if the survival fraction of the therapy is too high, rescue of the quiescent population occurs. This gives rise to emergence of resistance to therapy since the rescued population is less sensitive to therapy. R.C. and T.A. acknowledge the Ministry of Economy and Competitivity (MINECO) for funding under grant MTM2015-71509-C2-1-R and Generalitat de Catalunya for funding under grant 2014SGR1307. R.C. acknowledges AGAUR-Generalitat de Catalunya for funding under its doctoral scholarship programme. P.G. thanks the Wellcome Trust for financial support under grant 098325. T.A. acknowledges support from the Ministry of Economy & Competitivity (MINECO) for funding awarded to the Barcelona Graduate School of Mathematics under the "María de Maeztu" programme, grant number MDM-2014-0445. F.S. acknowledges the support of the NCI under grant number 5U01CA177799.

The goal of this work is to develop a numerical simulation that accurately captures the biomechanical response of bacterial biofilms and their associated extracellular matrix (ECM). In this, the second of a two-part effort, the primary focus is on formally presenting the heterogeneous rheology Immersed Boundary Method (hrIBM) and validating our model against experimental results. With this extension of the Immersed Bounadry Method (IBM), we use the techniques originally developed in Part I, (Hammond et al. (2014) ) to treat the biofilm as a viscoelastic fluid possessing variable rheological properties anchored to a set of moving locations (i.e., the bacteria locations). We validate our modeling approach from Part I by comparing dynamic moduli and compliance moduli computed from our model to data from mechanical characterization experiments on Staphylococcus epidermidis biofilms. The experimental setup is described in Pavlovsky et al. (2013) in which biofilms are grown and tested in a parallel plate rheometer. Matlab code used to produce results in this paper will be available at https://github.com/MathBioCU/BiofilmSim., 26 pages, 8 figures, 6 tables

We investigate a method of selectively targeting cancer cells by means of ultrasound harmonic excitation at their resonance frequency, which we refer to as oncotripsy. The geometric model of the cells takes into account the cytoplasm, nucleus and nucleolus, as well as the plasma membrane and nuclear envelope. Material properties are varied within a pathophysiologically-relevant range. A first modal analysis reveals the existence of a spectral gap between the natural frequencies and, most importantly, resonant growth rates of healthy and cancerous cells. The results of the modal analysis are verified by simulating the fully-nonlinear transient response of healthy and cancerous cells at resonance. The fully nonlinear analysis confirms that cancerous cells can be selectively taken to lysis by the application of carefully tuned ultrasound harmonic excitation while simultaneously leaving healthy cells intact., Comment: 22 pages

In this paper the first equation within a class of well known chemotaxis systems is derived as a hydrodynamic limit from a stochastic interacting many particle system on the lattice. The cells are assumed to interact with attractive chemical molecules on a finite number of lattice sites, but they only directly interact among themselves on the same lattice site. The chemical environment is assumed to be stationary with a slowly varying mean, which results in a non-trivial macroscopic chemotaxis equation for the cells. Methodologically the limiting procedure and its proofs are based on results by Koukkus [18] and Kipnis/Landim [17]. Numerical simulations extend and illustrate the theoretical findings., 21 pages, 16 figures

The effects of pulsatile GnRH stimulation on anterior pituitary cells are studied using perifusion cell cultures, where constantly moving culture medium over the immobilized cells allows intermittent GnRH delivery. The LH content of the outgoing medium serves as a readout of the GnRH signaling pathway activation in the cells. The challenge lies in relating the LH content of the medium leaving the chamber to the cellular processes producing LH secretion. To investigate this relation we developed and analyzed a mathematical model consisting of coupled partial differential equations describing LH secretion in a perifusion cell culture. We match the mathematical model to three different data sets and give cellular mechanisms that explain the data. Our model illustrates the importance of the negative feedback in the signaling pathway and receptor desensitization. We demonstrate that different LH outcomes in oxytocin and GnRH stimulations might originate from different receptor dynamics and concentration. We analyze the model to understand the influence of parameters, like the velocity of the medium flow or the fraction collection time, on the LH outcomes. We show that slow velocities lead to high LH outcomes. Also, we show that fraction collection times, which do not divide the GnRH pulse period evenly, lead to irregularities in the data. We examine the influence of the rate of binding and dissociation of GnRH on the GnRH movement down the chamber. Our model serves as an important tool that can help in the design of perifusion experiments and the interpretation of results.

In vitro cell proliferation assays are widely used in pharmacology, molecular biology, and drug discovery. Using theoretical modeling and experimentation, we show that current antiproliferative drug effect metrics suffer from time-dependent bias, leading to inaccurate assessments of parameters such as drug potency and efficacy. We propose the drug-induced proliferation (DIP) rate, the slope of the line on a plot of cell population doublings versus time, as an alternative, time-independent metric., Comment: 44 pages: main and supplementary text, 3 main text figures, 9 supplementary figures, 2 supplementary tables, Nature Methods, 2016 (advanced online publication)

"Secrete-and-sense cells" can communicate by secreting a signaling molecule while also producing a receptor that detects the molecule. The cell can potentially "talk" to itself ("self-communication") or talk to neighboring cells with the same receptor ("neighbor-communication"). The predominant forms of secrete-and-sense cells are self-communicating "autocrine cells" that are largely found in animals, and neighbor-communicating "quorum sensing cells" that are mostly associated with bacteria. While assumed to function independent of one another, recent studies have discovered quorum sensing organs and autocrine signaling microbes. Moreover, similar types of genetic circuits control many autocrine and quorum sensing cells. We outline these recent findings and explain how autocrine and quorum sensing are two sides of a many-sided "dice" created by the versatile secrete-and-sense cell., Review - 24 pages in total, including main text and 4 figures, Trends in Cell Biology (E-pub, ahead of print version) (December 2015)

Based on symmetry consideration of migration and shape deformations, we formulate phenomenologically the dynamics of cell crawling in two dimensions. Forces are introduced to change the cell shape. The shape deformations induce migration of the cell on a substrate. For time-independent forces we show that not only a stationary motion but also a limit cycle oscillation of the migration velocity and the shape occurs as a result of nonlinear coupling between different deformation modes. Time-dependent forces are generated in a stochastic manner by utilizing the so-called coherence resonance of an excitable system. The present coarse-grained model has a flexibility that it can be applied, e.g., both to keratocyte cells and to Dictyostelium cells, which exhibit quite different dynamics from each other. The key factors for the motile behavior inherent in each cell type are identified in our model.

In the framework of a phase field model of a single cell crawling on a substrate, we investigate how the properties of the cell membrane affect the shape and motility of the cell. Since the membrane influences the cell dynamics on multiple levels and provides a nontrivial feedback, we consider the following fundamental interactions: (i) the reduction of the actin polymerization rate by membrane tension; (ii) area conservation of the cell’s two-dimensional cross-section vs. conservation of the circumference (i.e. membrane inextensibility); and (iii) the contribution from the membrane’s bending energy to the shape and integrity of the cell. As in experiments, we investigate two pertinent observables — the cell’s velocity and its aspect ratio. We find that the most important effect is the feedback of membrane tension on the actin polymerization. Bending rigidity has only minor effects, visible mostly in dynamic reshaping events, as exemplified by collisions of the cell with an obstacle.

We present a single, unified, multi-scale model to study the attachment\detachment dynamics of two deforming, near spherical cells, coated with binding ligands and subject to a slow, homogeneous shear flow in a viscous fluid medium. The binding ligands on the surface of the cells experience attractive and repulsive forces in an ionic medium and exhibit finite resistance to rotation via bond tilting. The macroscale drag forces and couples describing the fluid flow inside the small separation gap between the cells, are calculated using a combination of methods in lubrication theory and previously published numerical results. For a select range of material and fluid parameters, a hysteretic transition of the sticking probability curves between the adhesion and fragmentation domain is attributed to a nonlinear relation between the total microscale binding forces and the separation gap between the cells. We show that adhesion is favored in highly ionic fluids, increased deformability of the cells, elastic binders and a higher fluid shear rate (until a critical value). Continuation of the limit points predict a bistable region, indicating an abrupt switching between the adhesion and fragmentation regimes at critical shear rates, and suggesting that adhesion of two deformable surfaces in shearing fluids may play a significant dynamical role in some cell adhesion applications., Comment: 23 pages, 11 figures

Single cells often generate precise responses by involving dissipative out-of-thermodynamic equilibrium processes in signaling networks. The available free energy to fuel these processes could become limited depending on the metabolic state of an individual cell. How does limiting dissipation affect the kinetics of high precision responses in single cells? I address this question in the context of a kinetic proofreading scheme used in a simple model of early time T cell signaling. I show using exact analytical calculations and numerical simulations that limiting dissipation qualitatively changes the kinetics in single cells marked by emergence of slow kinetics, large cell-to-cell variations of copy numbers, temporally correlated stochastic events (dynamic facilitation), and, ergodicity breaking. Thus, constraints in energy dissipation, in addition to negatively affecting ligand discrimination in T cells, can create a fundamental difficulty in interpreting single cell kinetics from cell population level results., Comment: Revised version. In press in Biophysical Journal

Herein, we use a facile procedure to graft a thin graphitic C3N4 (g-C3N4) layer on aligned TiO2 nanotube arrays (TiNT) by a one-step chemical vapor deposition (CVD) approach. This provides a platform to enhance the visible-light response of TiO2 nanotubes for antimicrobial applications. The formed g-C3N4/TiNT binary nanocomposite exhibits excellent bactericidal efficiency against Escherichia coli (E. coli) as a visible-light activated antibacterial coating, without the use of additional bactericides.

The paradigm of phenotypic plasticity indicates reversible relations of different cancer cell phenotypes, which extends the cellular hierarchy proposed by the classical cancer stem cell (CSC) theory. Since it is still question able if the phenotypic plasticity is a crucial improvement to the hierarchical model or just a minor extension to it, it is worthwhile to explore the dynamic behavior characterizing the reversible phenotypic plasticity. In this study we compare the hierarchical model and the reversible model in predicting the cell-state dynamics observed in biological experiments. Our results show that the hierarchical model shows significant disadvantages over the reversible model in describing both long-term stability (phenotypic equilibrium) and short-term transient dynamics (overshoot) of cancer cells. In a very specific case in which the total growth of population due to each cell type is identical, the hierarchical model predicts neither phenotypic equilibrium nor overshoot, whereas thereversible model succeeds in predicting both of them. Even though the performance of the hierarchical model can be improved by relaxing the specific assumption, its prediction to the phenotypic equilibrium strongly depends on a precondition that may be unrealistic in biological experiments, and it also fails to capture the overshoot of CSCs. By comparison, it is more likely for the reversible model to correctly describe the stability of the phenotypic mixture and various types of overshoot behavior., 24 pages, 6 figures

Multipotent differentiation, where cells adopt one of several cell fates, is a determinate and orchestrated procedure that often incorporates stochastic mechanisms in order to diversify cell types. How these stochastic phenomena interact to govern cell fate is poorly understood. Nonetheless, cell fate decision-making procedure is mainly regulated through the activation of differentiation waves and associated signaling pathways. In the current work, we focus on the Notch/Delta signaling pathway, which is not only known to trigger such waves but also is used to achieve the principle of lateral inhibition (i.e., a competition for exclusive fates through cross-signaling between neighboring cells). Such a process ensures unambiguous stochastic decisions influenced by intrinsic noise sources, such as those found in the regulation of signaling pathways, and extrinsic stochastic fluctuations attributed to microenvironmental factors. However, the effect of intrinsic and extrinsic noise on cell fate determination is an open problem. Our goal is to elucidate how the induction of extrinsic noise affects cell fate specification in a lateral inhibition mechanism. Using a stochastic Cellular Automaton with continuous state space, we show that extrinsic noise results in the emergence of steady-state furrow patterns of cells in a “frustrated/transient” phenotypic state.

Quantitative single cell measurements have shown that cell cycle duration (the time between cell divisions) for diverse cell types is a noisy variable. The underlying distribution is mean scalable with a universal shape for many cell types in a variety of environments. Here we show through both experiment and theory that increasing the amount of noise in the regulation of the cell cycle negatively impacts the growth rate but positively correlates with improved cellular response to fluctuating environments. Our findings suggest that even non-cooperative cells in exponential growth phase do not optimize fitness through growth rate alone, but also optimize adaptability to changing conditions. In a manner similar to genetic evolution, increasing the noise in biochemical processes correlates with improved response of the system to environmental changes., 5 pages, 4 figures

Cellular decision making allows cells to assume functionally different phenotypes in response to microenvironmental cues, with or without genetic change. It is an open question, how individual cell decisions influence the dynamics at the tissue level. Here, we study spatio-temporal pattern formation in a population of cells exhibiting phenotypic plasticity, which is a paradigm of cell decision making. We focus on the migration/resting and the migration/proliferation plasticity which underly the epithelial-mesenchymal transition and the go or grow dichotomy. We assume that cells change their phenotype in order to minimize their microenvironmental entropy following the LEUP (Least microEnvironmental Uncertainty Principle) hypothesis. In turn, we study the impact of the LEUP-driven migration/resting and migration/proliferation plasticity on the corresponding multicellular spatio-temporal dynamics with a stochastic cell-based mathematical model for the spatio-temporal dynamics of the cell phenotypes. In the case of the go or rest plasticity, a corresponding mean-field approximation allows to identify a bistable switching mechanism between a diffusive (fluid) and an epithelial (solid) tissue phase which depends on the sensitivity of the phenotypes to the environment. For the go or grow plasticity, we show the possibility of Turing pattern formation for the ‘solid’ tissue phase and its relation with the parameters of the LEUP-driven cell decisions.

Neurodegenerative diseases are closely associated with the amplification and invasion of toxic proteins. In particular Alzheimer's disease is characterized by the systematic progression of amyloid-$\beta$ and $\tau$-proteins in the brain. These two protein families are coupled and it is believed that their joint presence greatly enhances the resulting damage. Here, we examine a class of coupled chemical kinetics models of healthy and toxic proteins in two spatial dimensions. The anisotropic diffusion expected to take place within the brain along axonal pathways is factored in the models and produces a filamentary, predominantly one-dimensional transmission. Nevertheless, the potential of the anisotropic models towards generating interactions taking advantage of the two-dimensional landscape is showcased. Finally, a reduction of the models into a simpler family of generalized Fisher-Kolmogorov-Petrovskii-Piskunov (FKPP) type systems is examined. It is seen that the latter captures well the qualitative propagation features, although it may somewhat underestimate the concentrations of the toxic proteins., Comment: 11 pages, 8 figures

Mathematical modelling has successfully been used to provide quantitative descriptions of many viral infections, but for the Ebola virus, which requires biosafety level 4 facilities for experimentation, modelling can play a crucial role. Ebola virus modelling efforts have primarily focused on in vivo virus kinetics, e.g., in animal models, to aid the development of antivirals and vaccines. But, thus far, these studies have not yielded a detailed specification of the infection cycle, which could provide a foundational description of the virus kinetics and thus a deeper understanding of their clinical manifestation. Here, we obtain a diverse experimental data set of the Ebola virus infection in vitro, and then make use of Bayesian inference methods to fully identify parameters in a mathematical model of the infection. Our results provide insights into the distribution of time an infected cell spends in the eclipse phase (the period between infection and the start of virus production), as well as the rate at which infectious virions lose infectivity. We suggest how these results can be used in future models to describe co-infection with defective interfering particles, which are an emerging alternative therapeutic., Author summary The two deadliest Ebola virus epidemics have both occurred in the past five years, with one of these epidemics still ongoing. Mathematical modelling has already provided insights into the spread of disease at the population level as well as the effect of antiviral therapy in Ebola virus-infected animals. However, a quantitative description of the replication cycle is still missing. Here, we report results from a set of in vitro experiments involving infection with the Ecran strain of Ebola virus. By parameterizing a mathematical model, we are able to determine robust estimates for the duration of the replication cycle, the infectious burst size, and the viral clearance rate.

Eukaryotic cell motility involves a complex network of interactions between biochemical components and mechanical processes. The cell employs this network to polarize and induce shape changes that give rise to membrane protrusions and retractions, ultimately leading to locomotion of the entire cell body. The combination of a nonlinear reaction–diffusion model of cell polarization, noisy bistable kinetics, and a dynamic phase field for the cell shape permits us to capture the key features of this complex system to investigate several motility scenarios, including amoeboid and fan-shaped forms as well as intermediate states with distinct displacement mechanisms. We compare the numerical simulations of our model to live cell imaging experiments of motile Dictyostelium discoideum cells under different developmental conditions. The dominant parameters of the mathematical model that determine the different motility regimes are identified and discussed. © 2020 Elsevier B.V.

Biomaterial systems have allowed for the in vitro production of complex, emergent tissue behaviors that were not possible with conventional 2D culture systems allowing for analysis of the normal development as well as disease processes. We propose that the path towards developing the design parameters for biomaterial systems lies with identifying the molecular drivers of emergent behavior through leveraging technological advances in systems biology, including single cell omics, genetic engineering, and high content imaging. This research focus, which we term systems tissue engineering, can uniquely interrogate the mechanisms by which complex tissue behaviors emerge with the potential to capture the contribution of i) dynamic regulation of tissue development and dysregulation, ii) single cell heterogeneity and the function of rare cell types, and iii) the spatial distribution and structure of individual cells and cell types within a tissue. Collectively, systems tissue engineering can facilitate the identification of biomaterial design parameters that will accelerate basic science discovery and translation., 17 pages, 2 figures

Social interaction between microbes can be described at many levels of details: from the biochemistry of cell-cell interactions to the ecological dynamics of populations. Choosing an appropriate level to model microbial communities without losing generality remains a challenge. Here we show that modeling cross-feeding interactions at an intermediate level between genome-scale metabolic models of individual species and consumer-resource models of ecosystems is suitable to experimental data. We applied our modeling framework to three published examples of multi-strain Escherichia coli communities with increasing complexity: uni-, bi-, and multi-directional cross-feeding of either substitutable metabolic byproducts or essential nutrients. The intermediate-scale model accurately fit empirical data and quantified metabolic exchange rates that are hard to measure experimentally, even for a complex community of 14 amino acid auxotrophies. By studying the conditions of species coexistence, the ecological outcomes of cross-feeding interactions, and each community’s robustness to perturbations, we extracted new quantitative insights from these three published experimental datasets. Our analysis provides a foundation to quantify cross-feeding interactions from experimental data, and highlights the importance of metabolic exchanges in the dynamics and stability of microbial communities., Author summary The behavior of microbial communities such as the human microbiome is hard to predict by its species composition alone. Our efforts to engineer microbiomes—for example to improve human health—would benefit from mathematical models that accurately describe how microbes exchange metabolites with each other and how their environment shapes these exchanges. But what is an appropriate level of details for those models? We propose an intermediate level to model metabolic exchanges between microbes. We show that these models can accurately describe population dynamics in three laboratory communities and predicts their stability in response to perturbations such as changes in the nutrients available in the medium that they grow on. Our work suggests that a highly detailed metabolic network model is unnecessary for extracting ecological insights from experimental data and improves mathematical models so that one day we may be able to predict the behavior of real-world communities such as the human microbiome.

We provide a review of recent advancements in non-local continuous models for migration, mainly from the perspective of its involvement in embryonal development and cancer invasion. Particular emphasis is placed on spatial non-locality occurring in advection terms, used to characterize a cell’s motility bias according to its interactions with other cellular and acellular components in its vicinity (e.g. cell–cell and cell–tissue adhesions, non-local chemotaxis), but we also briefly address spatially non-local source terms. Following a short introduction and description of applications, we give a systematic classification of available PDE models with respect to the type of featured non-localities and review some of the mathematical challenges arising from such models, with a focus on analytical aspects. This article is part of the theme issue ‘Multi-scale analysis and modelling of collective migration in biological systems’.

Key traits of unicellular species, like cell size, often follow scale-free or self-similar distributions, hinting at the possibility of an underlying critical process. However, linking such empirical scaling laws to the critical regime of realistic individual-based model classes is difficult. Here we reveal new empirical scaling evidence associated with a transition in the population and chlorophyll dynamics of phytoplankton. We offer a possible explanation for these observations by deriving scaling laws in the vicinity of the critical point of a new universality class of non-local cell growth and division models. This `criticality hypothesis' can be tested through new scaling predictions derived for our model class, for the response of chlorophyll distributions to perturbations. The derived scaling laws may also be generalized to other cellular traits and environmental drivers relevant to phytoplankton ecology., Comment: Companion paper in BioRxiv https://doi.org/10.1101/679209

A mathematical model is proposed for shape evolution and locomotion of fish epidermal keratocytes on elastic substrates. The model is based on mechanosensing concepts: cells apply contractile forces onto the elastic substrate, while cell shape evolution depends locally on the substrate stress generated by themselves or external mechanical stimuli acting on the substrate. We use the level set method to study the behavior of the model numerically, and predict a number of distinct phenomena observed in experiments, such as (i) symmetry breaking from the stationary centrosymmetric to the well-known steadily propagating crescent shape, (ii) asymmetric bipedal oscillations and traveling waves in the lamellipodium leading edge (iii) response to mechanical stress externally applied to the substrate (tensotaxis), (iv) changing direction of motion towards an interface with a rigid substrate (durotaxis) and (v) the configuration of substrate wrinkles induced by contractile forces applied by the keratocyte., Comment: Additional materia, 14 pagesl, 9 figures, 38 references

We have experimentally investigated the transitions of collective motions of bacterial cells in a shallow circular pool using the bacterial species $Bacillus$ $subtilis$. In our previous paper, we reported that the collective motions were classified into six phases on a phase diagram with two parameters, namely, the reduced cell length $\lambda$ and the cell density $\rho$. In this study, we focused on the sharp transitions at $\lambda\cong0.1$ ($\equiv \lambda_{\rm C1}$) with low values of $\rho$ between the $random$ $motion$ phase and the $one$-$way$ $rotational$ $motion$ phase. By introducing the order parameter $Q$ which measures the aligned cell motion along the circumferential direction of a pool, the transitions at $\lambda=\lambda_{\rm C1}$ were clearly characterized. On the basis of the detailed observations of single-cell trajectories in a pool, we verified that the effect of cell$-$noise interactions was widely distributed. We conclude that, even in such random environment, the sharp transitions of collective motions were caused by the cell$-$cell interactions at $\lambda=\lambda_{\rm C1}$., Comment: v2: LaTeX2e, 18 pages, 9 figures, revised version for publication in J. Phys. Soc. Jpn

It has been shown recently that changing the fluidic properties of a drug can improve its efficacy in ablating solid tumors. We develop a modeling framework for tumor ablation, and present the simplest possible model for drug diffusion in a spherical tumor with leaky boundaries and assuming cell death eventually leads to ablation of that cell effectively making the two quantities numerically equivalent. The death of a cell after a given exposure time depends on both the concentration of the drug and the amount of oxygen available to the cell. Higher oxygen availability leads to cell death at lower drug concentrations. It can be assumed that a minimum concentration is required for a cell to die, effectively connecting diffusion with efficacy. The concentration threshold decreases as exposure time increases, which allows us to compute dose-response curves. Furthermore, these curves can be plotted at much finer time intervals compared to that of experiments, which is used to produce a dose-threshold-response surface giving an observer a complete picture of the drug's efficacy for an individual. In addition, since the diffusion, leak coefficients, and the availability of oxygen is different for different individuals and tumors, we produce artificial replication data through bootstrapping to simulate error. While the usual data-driven model with Sigmoidal curves use 12 free parameters, our mechanistic model only has two free parameters, allowing it to be open to scrutiny rather than forcing agreement with data. Even so, the simplest model in our framework, derived here, shows close agreement with the bootstrapped curves, and reproduces well established relations, such as Haber's rule., Comment: 25 pages, 65 figures, 2 tables

Topological and geometrical properties and the associated topological defects find a rapidly growing interest in studying the interplay between mechanics and the collective behavior of cells on the tissue level. We here test if well studied equilibrium laws for polydisperse passive systems such as the Lewis's and the Aboav-Weaire's law are applicable also for active cellular structures. Large scale simulations, which are based on a multi phase field active polar gel model, indicate that these active cellular structures follow these laws. If the system is in a state of collective motion also quantitative agreement with typical values for passive systems is observed. If this state has not developed quantitative differences can be found. We further compare the model with discrete modeling approaches for cellular structures and show that essential properties, such as T1 transitions and rosettes are naturally fulfilled., 6 pages, 6 figures

Neuroinflammation in utero may result in lifelong neurological disabilities. Astrocytes play a pivotal role, but the mechanisms are poorly understood. No early postnatal treatment strategies exist to enhance neuroprotective potential of astrocytes. We hypothesized that agonism on alpha7 nicotinic acetylcholine receptor (alpha7nAChR) in fetal astrocytes will augment their neuroprotective transcriptome profile, while the antagonistic stimulation of alpha7nAChR will achieve the opposite. Using an in vivo - in vitro model of developmental programming of neuroinflammation induced by lipopolysaccharide (LPS), we validated this hypothesis in primary fetal sheep astrocytes cultures re-exposed to LPS in presence of a selective alpha7nAChR agonist or antagonist. Our RNAseq findings show that a pro-inflammatory astrocyte transcriptome phenotype acquired in vitro by LPS stimulation is reversed with alpha7nAChR agonistic stimulation. Conversely, antagonistic alpha7nAChR stimulation potentiates the pro-inflammatory astrocytic transcriptome phenotype. Furthermore, we conduct a secondary transcriptome analysis against the identical alpha7nAChR experiments in fetal sheep primary microglia cultures and discuss the implications for neurodevelopment., See also the accompanying repository on GitHub: https://github.com/martinfrasch/astrocytes_RNAseq

In this work we prove occurrence of a super-critical Hopf bifurcation in a model of white blood cell formation structured by three maturation stages. We provide an explicit analytical expression for the bifurcation point depending on model parameters. The Hopf bifurcation is a unique feature of the multi-compartment structure as it does not exist in the corresponding two-compartment model. It appears for a parameter set different from the parameters identified for healthy hematopoiesis and requires changes in at least two cell properties. Model analysis allows identifying a range of biologically plausible parameter sets that can explain persistent oscillations of white blood cell counts observed in some hematopoietic diseases. Relating the identified parameter sets to recent experimental and clinical findings provides insights into the pathological mechanisms leading to oscillating blood cell counts., 34 pages, 5 figures, 2 tables; new references added, new figure added, typos corrected

We study a simple run-and-tumble random walk whose switching frequency from run mode to tumble mode and the reverse depend on a stochastic signal. We consider a particularly sharp, step-like dependence, where the run to tumble switching probability jumps from zero to one as the signal crosses a particular value (say y_1 ) from below. Similarly, tumble to run switching probability also shows a jump like this as the signal crosses another value (y_2 < y_1 ) from above. We are interested in characterizing the effect of signaling noise on the long time behavior of the random walker. We consider two different time-evolutions of the stochastic signal. In one case, the signal dynamics is an independent stochastic process and does not depend on the run-and-tumble motion. In this case we can analytically calculate the mean value and the complete distribution function of the run duration and tumble duration. In the second case, we assume that the signal dynamics is influenced by the spatial location of the random walker. For this system, we numerically measure the steady state position distribution of the random walker. We discuss some similarities and differences between our system and E.coli chemotaxis, which is another well-known run-and-tumble motion encountered in nature., Published in Physical Rev. E

Mitochondrial networks exhibit a variety of complex behaviors, including coordinated cell-wide oscillations of energy states as well as a phase transition (depolarization) in response to oxidative stress. Since functional and structural properties are often interwinded, here we characterized the structure of mitochondrial networks in mouse embryonic fibroblasts using network tools and percolation theory. Subsequently we perturbed the system either by promoting the fusion of mitochondrial segments or by inducing mitochondrial fission. Quantitative analysis of mitochondrial clusters revealed that structural parameters of healthy mitochondria laid in between the extremes of highly fragmented and completely fusioned networks. We confirmed our results by contrasting our empirical findings with the predictions of a recently described computational model of mitochondrial network emergence based on fission-fusion kinetics. Altogether these results offer not only an objective methodology to parametrize the complexity of this organelle but also support the idea that mitochondrial networks behave as critical systems and undergo structural phase transitions. Fil: Zamponi, Emiliano. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Investigación Médica Mercedes y Martín Ferreyra. Universidad Nacional de Córdoba. Instituto de Investigación Médica Mercedes y Martín Ferreyra; Argentina Fil: Zamponi, Nahuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Investigación Médica Mercedes y Martín Ferreyra. Universidad Nacional de Córdoba. Instituto de Investigación Médica Mercedes y Martín Ferreyra; Argentina Fil: Cannas, Sergio Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina Fil: Billoni, Orlando Vito. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina Fil: Helguera, Pablo Rodolfo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Investigación Médica Mercedes y Martín Ferreyra. Universidad Nacional de Córdoba. Instituto de Investigación Médica Mercedes y Martín Ferreyra; Argentina Fil: Chialvo, Dante Renato. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de San Martín; Argentina

Significance Pattern formation is a central question in developmental biology. Alan Turing proposed that this could be achieved by a diffusion-driven instability in a monophasic system consisting of two reacting chemicals. In this paper, we extend Turing’s work to a more realistic mechanochemical model of multicellular tissue, modeling also its biphasic and mechanical properties. Overcoming limitations of conventional reaction–diffusion models, we show that mechanochemical couplings between morphogen concentrations and extracellular fluid flows provide alternative, non-Turing, mechanisms by which tissues can form robust spatial patterns., The formation of self-organized patterns is key to the morphogenesis of multicellular organisms, although a comprehensive theory of biological pattern formation is still lacking. Here, we propose a minimal model combining tissue mechanics with morphogen turnover and transport to explore routes to patterning. Our active description couples morphogen reaction and diffusion, which impact cell differentiation and tissue mechanics, to a two-phase poroelastic rheology, where one tissue phase consists of a poroelastic cell network and the other one of a permeating extracellular fluid, which provides a feedback by actively transporting morphogens. While this model encompasses previous theories approximating tissues to inert monophasic media, such as Turing’s reaction–diffusion model, it overcomes some of their key limitations permitting pattern formation via any two-species biochemical kinetics due to mechanically induced cross-diffusion flows. Moreover, we describe a qualitatively different advection-driven Keller–Segel instability which allows for the formation of patterns with a single morphogen and whose fundamental mode pattern robustly scales with tissue size. We discuss the potential relevance of these findings for tissue morphogenesis.

Funding: N.S was partially supported by the German Science Foundation (DFG) under the grant SFB 873 “Maintenance and Differentiation of Stem Cells in Development and Disease”. We extend the live-cell motility Filament Based Lamellipodium Model to incorporate the forces exerted on the lamellipodium of the cells due to cell-cell collision and cadherin induced cell-cell adhesion. We take into account the nature of these forces via physical and biological constraints and modelling assumptions. We investigate the effect these new components have in the migration and morphology of the cells through particular experiments. We exhibit moreover the similarities between our simulated cells and HeLa cancer cells. Publisher PDF

While most processes in biology are highly deterministic, stochastic mechanisms are sometimes used to increase cellular diversity. In human and Drosophila eyes, photoreceptors sensitive to different wavelengths of light are distributed in stochastic patterns, and one such patterning system has been analyzed in detail in the Drosophila retina. Interestingly, some species in the dipteran family Dolichopodidae (the “long legged” flies, or “Doli”) instead exhibit highly orderly deterministic eye patterns. In these species, alternating columns of ommatidia (unit eyes) produce corneal lenses of different colors. Occasional perturbations in some individuals disrupt the regular columns in a way that suggests that patterning occurs via a posterior-to-anterior signaling relay during development, and that specification follows a local, cellular-automaton-like rule. We hypothesize that the regulatory mechanisms that pattern the eye are largely conserved among flies and that the difference between unordered Drosophila and ordered dolichopodid eyes can be explained in terms of relative strengths of signaling interactions rather than a rewiring of the regulatory network itself. We present a simple stochastic model that is capable of explaining both the stochastic Drosophila eye and the striped pattern of Dolichopodidae eyes and thereby characterize the least number of underlying developmental rules necessary to produce both stochastic and deterministic patterns. We show that only small changes to model parameters are needed to also reproduce intermediate, semi-random patterns observed in another Doli species, and quantification of ommatidial distributions in these eyes suggests that their patterning follows similar rules., [Author summary] A simple model is able to account for a diversity of photoreceptor patterns in different fly species, ranging from highly deterministic to fully random., This work was supported in part by German research foundation STA 850/15-1 to PFS, NIH (grant R01 EY13010) to CD, NIH grant K99 EY027016 to MP Ministerio de Economía, Industria y Competitividad http://www.mineco.gob.es/ through the Ramón y Cajal program and through project SPASIMM, FIS2016-80067-P (AEI/FEDER, EU) to KK.

Cells move by run and tumble, a kind of dynamics in which the cell alternates runs over straight lines and re-orientations. This erratic motion may be influenced by external factors, like chemicals, nutrients, the extra-cellular matrix, in the sense that the cell measures the external field and elaborates the signal eventually adapting its dynamics. We propose a kinetic transport equation implementing a velocity-jump process in which the transition probability takes into account a double bias, which acts, respectively, on the choice of the direction of motion and of the speed. The double bias depends on two different non-local sensing cues coming from the external environment. We analyze how the size of the cell and the way of sensing the environment with respect to the variation of the external fields affect the cell population dynamics by recovering an appropriate macroscopic limit and directly integrating the kinetic transport equation. A comparison between the solutions of the transport equation and of the proper macroscopic limit is also performed.

We study the dynamics of a thick polar epithelium subjected to the action of both an electric and a flow field in a planar geometry. We develop a generalized continuum hydrodynamic description and describe the tissue as a two component fluid system. The cells and the interstitial fluid are the two components and we keep all terms allowed by symmetry. In particular we keep track of the cell pumping activity for both solvent flow and electric current and discuss the corresponding orders of magnitude. We study the growth dynamics of tissue slabs, their steady states and obtain the dependence of the cell velocity, net cell division rate, and cell stress on the flow strength and the applied electric field. We find that finite thickness tissue slabs exist only in a restricted region of phase space and that relatively modest electric fields or imposed external flows can induce either proliferation or death., Comment: 18 pages, 12 figures

The non-linear behavior of human erythrocytes subjected to shear stress was analyzed using data series from the Erythrocyte Rheometer and a theoretical model was developed. Linear behavior was eliminated by means of a slot filter and a sixth order Savisky-Golay filter was applied to the resulting time series that allows the elimination of any possible white noise in the data. A fast Fourier transform was performed on the processed data, which resulted in a series of frequency dominant peaks. Results suggest the presence of a non-linear quadratic term in the Kelvin- Voigt phenomenological model. The correlation dimension studied through recurrence quantification analysis gave C2=(2.58±0.08). Results suggest that the underlying dynamics is the same in each RBC sample corresponding to healthy donors. Fil: Castellini, Horacio V. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura. Departamento de Física; Argentina. Fil: Riquelme, Bibiana Doris. Universidad Nacional de Rosario. Facultad de Ciencias Bioquímicas y Farmacéuticas. Instituto de Física Rosario (IFIR-CONICET); Argentina.

In cell extrusion, a cell embedded in an epithelial monolayer loses its apical or basal surface and is subsequently squeezed out of the monolayer by neighboring cells. Cell extrusions occur during apoptosis, epithelial-mesenchymal transition, or pre-cancerous cell invasion. They play important roles in embryogenesis, homeostasis, carcinogenesis, and many other biological processes. Although many of the molecular factors involved in cell extrusion are known, little is known about the mechanical basis of cell extrusion. We used a three-dimensional (3D) vertex model to investigate the mechanical stability of cells arranged in a monolayer with 3D foam geometry. We found that when the cells composing the monolayer have homogeneous mechanical properties, cells are extruded from the monolayer when the symmetry of the 3D geometry is broken due to an increase in cell density or a decrease in the number of topological neighbors around single cells. Those results suggest that mechanical instability inherent in the 3D foam geometry of epithelial monolayers is sufficient to drive epithelial cell extrusion. In the situation where cells in the monolayer actively generate contractile or adhesive forces under the control of intrinsic genetic programs, the forces act to break the symmetry of the monolayer, leading to cell extrusion that is directed to the apical or basal side of the monolayer by the balance of contractile and adhesive forces on the apical and basal sides. Although our analyses are based on a simple mechanical model, our results are in accordance with observations of epithelial monolayers {\it in vivo} and consistently explain cell extrusions under a wide range of physiological and pathophysiological conditions. Our results illustrate the importance of a mechanical understanding of cell extrusion and provide a basis by which to link molecular regulation to physical processes., 16 pages, 5 figures. Biophysical Journal (2020)

Flux of rigid or soft particles (such as drops, vesicles, red blood cells, etc.) in a channel is a complex function of particle concentration, which depends on the details of induced dissipation and suspension structure due to hydrodynamic interactions with walls or between neighboring particles. Through two-dimensional and three-dimensional simulations and a simple model that reveals the contribution of the main characteristics of the flowing suspension, we discuss the existence of an optimal volume fraction for cell transport and its dependence on the cell mechanical properties. The example of blood is explored in detail, by adopting the commonly used modeling of red blood cells dynamics. We highlight the complexity of optimization at the level of a network, due to the antagonist evolution of local volume fraction and optimal volume fraction with the channels diameter. In the case of the blood network, the most recent results on the size evolution of vessels along the circulatory network of healthy organs suggest that the red blood cell volume fraction (hematocrit) of healthy subjects is close to optimality, as far as transport only is concerned. However, the hematocrit value of patients suffering from diverse red blood cel pathologies may strongly deviate from optimality., Comment: arXiv admin note: substantial text overlap with arXiv:1802.05353

Mechanical forces influence the dynamics of growing tissues. Computer simulations are employed to study the importance of interfacial effects in tissue competition. It was speculated previously that mechanical pressure determines the competition, where the determining quantity is the homeostatic pressure - the pressure where division and apoptosis balance; the tissue with the higher homeostatic pressure overwhelms the other. In contrast, we find that a weaker tissue can persist in stable coexistence with a stronger tissue, if adhesion between them is small enough. An analytic continuum description can quantitatively describe the underlying mechanism and reproduce the resulting pressures and cell-number fractions. Furthermore, simulations reveal a variety of coexisting structures, ranging from spherical inclusions to a bicontinuous state.

The study and applications of ferroelectric materials in the biomedical and biotechnological fields is a novel and very promising scientific area that spans roughly one decade. However, some groups have already provided experimental proof of very interesting biological modulation when living systems are exposed to different ferroelectrics and excitation mechanisms. These materials should offer several advantages in the field of bioelectricity, such as no need of an external electric power source or circuits, scalable size of the electroactive regions, flexible and reconfigurable virtual electrodes, or fully proved biocompatibility. In this focused review we provide the underlying physics of ferroelectric activity and a recount of the research reports already published, along with some tentative biophysical mechanisms that can explain the observed results. More specifically, we focused on the biological actions of domain ferroelectrics, and ferroelectrics excited by the bulk photovoltaic effect or the pyroelectric effect. It is our goal to provide a comprehensive account of the published material so far, and to set the stage for a vigorous expansion of the field, with envisioned applications that span from cell biology and signaling to cell and tissue regeneration, antitumoral action, or cell bioengineering to name a few., 39 pages, 10 figures, 3 tables, 127 references, publication year 2018

Collective oscillation of cells in a population has been reported under diverse biological contexts and with vastly different molecular constructs. Could there be common principles similar to those that govern spontaneous oscillation in mechanical or electrical systems? Here, we answer this question in the affirmative by categorising the response of individual cells against a time-varying signal. A positive intracellular signal relay of sufficient gain from participating cells is required to sustain the oscillations, together with phase matching. The two conditions yield quantitative predictions for the onset cell density and frequency in terms of measured single-cell and signal response functions. Through mathematical constructions, we show that cells that adapt to a constant stimulus fulfil the phase requirement by developing a leading phase in an "active" frequency window that enables cell-to-signal energy flow. Analysis of dynamical quorum sensing in several cellular systems with increasing biological complexity reaffirms the pivotal role of adaptation in powering oscillations in an otherwise dissipative cell-to-cell communication channel. The physical conditions identified can be used to design synthetic oscillatory systems, 11 pages and 6 figures for the main text. 18 pages and 14 figures for supplementary

Receptor-mediated endocytosis is an ubiquitous process through which cells internalize biological or synthetic nanoscale objects, including viruses, unicellular parasites, and nanomedical vectors for drug or gene delivery. In passive endocytosis the cell plasma membrane wraps around the "invader" particle driven by ligand-receptor complexation. By means of theory and numerical simulations, here we demonstrate how particles decorated by freely diffusing and non-mutually-interacting (ideal) ligands are significantly more difficult to wrap than those where ligands are either immobile or interact sterically with each other. Our model rationalizes the relationship between uptake mechanism and structural details of the invader, such as ligand size, mobility and ligand/receptor affinity, providing a comprehensive picture of pathogen endocytosis and helping the rational design of efficient drug delivery vectors., Comment: Updated version of the manuscript. Accepted for publication in PRE

Multiple myeloma (MM), a plasma cell cancer, is associated with many health challenges, including damage to the kidney by tubulointerstitial fibrosis. We develop a mathematical model which captures the qualitative behavior of the cell and protein populations involved. Specifically, we model the interaction between cells in the proximal tubule of the kidney, free light chains, renal fibroblasts, and myeloma cells. We analyze the model for steady-state solutions to find a mathematically and biologically relevant stable steady-state solution. This foundational model provides a representation of dynamics between key populations in tubulointerstitial fibrosis that demonstrates how these populations interact to affect patient prognosis in patients with MM and renal impairment., Included version of model without tumor with steady-state analysis, corrected equations for free light chains and renal fibroblasts in model with tumor to reflect steady-state analysis, updated abstract, updated and added references

Adaptive immunity is analogous to machine learning as the immune system learns about dangerous pathogens and discriminates them from safe self-molecules. Each immune cell has a unique receptor for specific immunological recognition. The binding affinity between the receptors and antigenic peptides mainly determines immunological recognition followed by subsequent responses. Is the integrated binding affinity sufficient to probe the digital information of peptide sequences? To answer this fundamental question, we examined whether the affinity-based discrimination of peptide sequences is learnable and generalizable by artificial neural networks (ANNs) that process the digital information of receptors and peptides. We made use of large scale high-throughput data of T-cell receptors (TCRs) and open-source peptides amino acid sequences as the input layer data, and computationally examined the success and failure of immune recognition based on the pairwise binding energy of their amino acid sequences as output layer data. Machine learning successfully captured the relevant information of molecular interactions and discriminated between strong and weak affinity pairs. This suggests the potential applicability of artificial neural networks to predict the immune responsiveness of certain antigenic peptides once their sequence information is provided. In addition, we used two methods to describe amino acids: with and without considering the amino acid strength. The sequences with heterogeneous strengths of amino acids diminished TCR "reading" of the exact information of each amino acid site on the peptides for the immune response. This may be why natural TCRs have moderate amino acid compositions after thymic selection.